首页|Diffusion approximation of Levy processes with a view towards finance
Diffusion approximation of Levy processes with a view towards finance
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NETL
NSTL
Walter De Gruyter
Let the (log-)prices of a collection of securities be given by a d-dimensional Levy process X_t having infinite activity and a smooth density. The value of a European contract with payoff g(x) maturing at T is determined by E[g(X_T)]. Let X_t be a finite activity approximation to X_T, where diffusion is introduced to approximate jumps smaller than a given truncation level ∈ > 0. The main result of this work is a derivation of an error expansion for the resulting model error, E[g{X_T) - g{X_T)], with computable leading order term. Our estimate depends both on the choice of truncation level e and the contract payoff g, and it is valid even when g is not continuous. Numerical experiments confirm that the error estimate is indeed a good approximation of the model error. Using similar techniques we indicate how to construct an adaptive truncation type approximation. Numerical experiments indicate that a substantial amount of work is to be gained from such adaptive approximation. Finally, we extend the previous model error estimates to the case of Barrier options, which have a particular path dependent structure.
Institute for Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden
Applied Mathematics and Computational Sciences, 4700 King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia
NETL
NSTL
Walter De Gruyter
